Main steps in the computation of the potential from Eqs. (25) and (27) in a typical case: a) the integral of the cool kernel, b) the integral of the hyperkernel, c) its vertical gradient, and d) the potential as the sum of maps a) and c). Here, the body is an axially symmetric torus with square cross section (boundary indicated with a white line). As clearly visible in graphs a)–c), the treatment differs slightly on the polar axis (first column of pixels). See the text for the numerical setup.